Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#14523236 | C2 | semidirect |
| 2. C2×C4×Dic254 | C2 | semidirect |
| 3. #22550073 | C2 | direct (N × H) |
| 4. C2×C4⋊(C127⋊C8) | C2 | semidirect |
| 5. C2×#16861130 | C2 | semidirect |
| 9. C2×#14523236 | C22 | semidirect |
| 12. C4×Dic254 | C22 | semidirect |
| 16. C4⋊(C127⋊C8) | C22 | semidirect |
| 17. #16861130 | C22 | semidirect |
| 26. C2×Dic254 | D4 | semidirect |
| 53. Dic254 | C2×D4 | semidirect |
| 70. C2×C4×C127 | SD16 | semidirect |
| 87. C4×C127 | C2×SD16 | semidirect |
| 93. C2×C127 | #460 | semidirect |
| 98. C127 | C2×#460 | semidirect |
| 167. C2×C4 | #14523236 | semidirect |
| 187. C4 | C2×#14523236 | semidirect |
| 191. C2 | #22550073 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523236 | 2 |
| C2×C4×Dic254 | 2 |
| #22550073 | 2 |
| C2×C4⋊(C127⋊C8) | 2 |
| C2×#16861130 | 2 |
| C2×#127×C127 | 2 |
| C2×#460 | 127 |